There are extensive hiking and climbing opportunities in nearby Parque Nacional Los Glaciares [1].
From here, it’s possible to arrange a one-day trek and ice climb on Glaciar Torre (US$85 pp) with Fitz Roy Expediciones (Avenida San Martín 56, tel. 02962/49-3017, www.fitzroyexpediciones.com.ar [2]), which also offers lengthier guided hikes—nine-day expeditions, really—on the Campo de Hielo Sur, the Southern Continental Ice Field.
Oscar Pandolfi Expediciones (Calle 2 No. 23, tel. 02962/49-3043, www.caminoabierto.com [3]) and Alta Montaña (Lionel Terray 55, tel. 02962/49-3018, altamont [at] infovia [dot] com [dot] ar) are also guides.
NYCA Adventure (Cabo García 122, tel. 02962/49-3185, www.nyca.com.ar [4]) offers half-day excursions that include activities such as climbing, hiking, mountain biking, rafting, and rappelling.
Lago San Martín (Avenida San Martín 275, tel. 02962/49-3045) arranges excursions to and from Lago San Martín, across the mountains to the northeast, with estancia accommodations.
The Casa de Guías (Avenida San Martín 310, tel. 02962/49-3118, www.casadeguias.com.ar [5]) is another possibility.
Just north of Albergue Rancho Grande, Viento Oeste (San Martín 898, tel. 02962/49-3200, vientooeste [at] infovia [dot] com [dot] ar) rents and sells climbing, camping, and wet-weather gear, as does La Brecha (Costanera Sur 246, tel. 02962/49-3151).
Eolia (Pasaje Fonrouge 45, tel. 02962/49-3066, www.patagoniamagica.com [6]) also rents gear and provides guide service.
Links:
[1] http://www.moon.com/destinations/argentina/southern-patagonia/interior-santa-cruz-province/parque-nacional-los-glaciares
[2] http://www.fitzroyexpediciones.com.ar
[3] http://www.caminoabierto.com
[4] http://www.nyca.com.ar
[5] http://www.casadeguias.com.ar
[6] http://www.patagoniamagica.com